WASHINGTON (CNN) -- Raising money and thinking about a running mate are two of the big challenges facing likely Republican presidential nominee John McCain.

Sen. John McCain's team will move to a campaign focused more on Democrats and the general election.

Both are on the agenda as the McCain team plans a transition to a campaign focused more on the Democrats and the general election. But one -- fundraising -- is being treated with considerably more urgency.

Sources involved in the effort say the McCain fundraising operation is reaching out to some 300 major Republican fundraisers, many of whom were supporting other GOP presidential candidates.

Also on the list are top fundraisers for President Bush's political organization. Top Bush fundraiser Mercer Reynolds, for example, endorsed McCain this past week, and campaign aides say he's actively helping to expand McCain's financial network.

The goal is to raise millions -- tens of millions -- by tapping these fundraising networks and finding donors who may have given the maximum amount to their first choice in the GOP field but have yet to give to McCain.

It's an effort proceeding on two tracks: raising millions for the "primary" campaign that continues up to the nominating convention this summer, while also beginning to amass millions more for the general election campaign.

Meanwhile, sources inside and close to the McCain camp acknowledge some casual conversations about a vice presidential search process. These sources stress emphatically that there have been no official meetings or discussions with McCain or even among his senior staff, though they expect the subject to come up in a series of transition meetings over the next several days and weeks.

"It is a top concern of the media and a relatively low concern of ours," one senior McCain adviser said. One reason for the lack of urgency: While McCain is the all-but-certain GOP nominee, the Democratic race is anything but clear -- and McCain is unlikely to make his pick until after the Democratic nominee chooses a running mate.

The Republican convention is a week after the Democrats', and while GOP sources don't rule out a McCain choice earlier, they say that under no circumstances would McCain pick a running mate without first knowing who would lead the Democratic ticket.

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Still, there are informal conversations about how to begin a search process.

Again, the sources said no decisions have been made. But several McCain aides and advisers who spoke to CNN on condition of anonymity suggest a logical choice to shepherd the process, at least at the beginning, is McCain adviser and veteran GOP strategist Charlie Black. In a brief conversation with CNN, Black said the subject has not come up in any of his conversations with McCain or campaign manager Rick Davis.

Others have suggested Davis would lead the process, though most in the campaign suggest he is too busy with day-to-day challenges, including expanding the staff to prepare for a national campaign, thinking ahead to the GOP convention and preparing for conversations with the Republican National Committee about installing a number of McCain operatives in the party's staff structure.

Those who discussed the running mate issue said that for now, the goal would be, as one put it, "to come up with a list of 20 or 25 people as your starting point and begin the basic research and early vetting."

So what does McCain need to do with his choice?

"Try back in June or July," one campaign official said with a laugh.

But GOP circles, of course, are full of such conversations. Some suggest former Arkansas Gov. Mike Huckabee's continued strong showing among social conservatives suggests McCain needs to shore up his right flank. Others say his choice will matter more than most vice presidential picks because McCain is 71 years old, so there will even more than the traditional scrutiny of whether the pick is up to being president. E-mail to a friend